TY - BOOK

T1 - Operation, Investment and Hedging in Electricity Markets

AU - Ernstsen, Rune Ramsdal

PY - 2016

Y1 - 2016

N2 - This thesis consists of an introduction as well as four papers. The papersconcern different problems associated to future electricity markets and thetopics include risk management, investment strategies, valuation and modelcalibration. Each paper is presented in a separate chapter and hence thechapters are self-contained and may be read individually. A more thoroughoverview is presented in Chapter 1.In Chapter 2 we consider a hedging problem for a power distributor deliveringelectricity on fixed price contracts in the Nordic electricity market andthereby being exposed to volume risk. We develop time series models for theelectric load, system price and deviation from system price. The model isdesigned such that for independent electric load, system price and deviationsfrom system price, the minimal variance hedge coincide with the standardpractice of the industry. We extend the model to include price and load correlationwhich results in an explicit strategy that reduces the variance. Tofurther improve the strategy we include autocorrelation and solve the hedgingproblem numerically and show that there is a large potential in changing riskmeasure and utilizing the skewness in the payoff distribution.In Chapter 3 we consider an investment problem for a strategic investorand a social planner with the opportunity to invest in inflexible and flexiblegeneration. We study the impact of market power and conjectured marketchanges with a simple price model based on linear demand response. We showthat the strategic investor invests later and in less capacity than the sociallyoptimal and that with increased market ownership investment is delayed furtherand capacity increased slightly. Furthermore, we find that an increase inmarket share for the strategic investor delays inflexible generation more thanflexible generation due to the exposure to potential low prices.In Chapter 4 we study the valuation of three representative generationtypes, an inflexible wind turbine, a flexible gas fired power plant and a hydroelectricplant that allows for storage. We account for the special characteristicsof each technology and include uncertainty in both price and volumethrough diffusion or jump diffusion models. We find explicit expressions forthe expected instantaneous value of wind generation as a function of electricityprice and wind speed. We include startup and shutdown costs for the gasfired power plant determine the startup and shutdown triggers as well as thevalue of the plant by maximizing the value of shutting down. This is done analyticallyin the diffusion models and numerically in the jump diffusion model.For the hydroelectric power plant we relax storage level and discharge constraintsusing penalty functions and linearize the optimal strategy from theHamilton-Jacobi-Bellman equation. This allows for closed form expressions ofthe value in terms of the expected price, the second moment of the price andthe autovariance of the price. We calibrate the models to 7 years of hourlyprice and wind data, determine the value and study the impact of anticipatedmarket changes on the value of the three types of generation.In Chapter 5 we develop an EM-algorithm with two jump componentssuch that the jump density of the compound Poisson process is a mixtureof two normal distributions. We show that each step of the EM-algorithmincreases the log-likelihood of the observed data by maximizing the expectationof the log-likelihood for the complete data conditional on the observeddata. We determine explicit expressions for the maximization step in termsof simple conditional expectations and present an approach for determiningthe conditional expectations. Finally, by applying the algorithm to calibratethe jump diffusion model from Chapter 4, we demonstrate that the additionaljump component provides a significantly better model of the observed datathan a model without jumps and with only a single jump component.

AB - This thesis consists of an introduction as well as four papers. The papersconcern different problems associated to future electricity markets and thetopics include risk management, investment strategies, valuation and modelcalibration. Each paper is presented in a separate chapter and hence thechapters are self-contained and may be read individually. A more thoroughoverview is presented in Chapter 1.In Chapter 2 we consider a hedging problem for a power distributor deliveringelectricity on fixed price contracts in the Nordic electricity market andthereby being exposed to volume risk. We develop time series models for theelectric load, system price and deviation from system price. The model isdesigned such that for independent electric load, system price and deviationsfrom system price, the minimal variance hedge coincide with the standardpractice of the industry. We extend the model to include price and load correlationwhich results in an explicit strategy that reduces the variance. Tofurther improve the strategy we include autocorrelation and solve the hedgingproblem numerically and show that there is a large potential in changing riskmeasure and utilizing the skewness in the payoff distribution.In Chapter 3 we consider an investment problem for a strategic investorand a social planner with the opportunity to invest in inflexible and flexiblegeneration. We study the impact of market power and conjectured marketchanges with a simple price model based on linear demand response. We showthat the strategic investor invests later and in less capacity than the sociallyoptimal and that with increased market ownership investment is delayed furtherand capacity increased slightly. Furthermore, we find that an increase inmarket share for the strategic investor delays inflexible generation more thanflexible generation due to the exposure to potential low prices.In Chapter 4 we study the valuation of three representative generationtypes, an inflexible wind turbine, a flexible gas fired power plant and a hydroelectricplant that allows for storage. We account for the special characteristicsof each technology and include uncertainty in both price and volumethrough diffusion or jump diffusion models. We find explicit expressions forthe expected instantaneous value of wind generation as a function of electricityprice and wind speed. We include startup and shutdown costs for the gasfired power plant determine the startup and shutdown triggers as well as thevalue of the plant by maximizing the value of shutting down. This is done analyticallyin the diffusion models and numerically in the jump diffusion model.For the hydroelectric power plant we relax storage level and discharge constraintsusing penalty functions and linearize the optimal strategy from theHamilton-Jacobi-Bellman equation. This allows for closed form expressions ofthe value in terms of the expected price, the second moment of the price andthe autovariance of the price. We calibrate the models to 7 years of hourlyprice and wind data, determine the value and study the impact of anticipatedmarket changes on the value of the three types of generation.In Chapter 5 we develop an EM-algorithm with two jump componentssuch that the jump density of the compound Poisson process is a mixtureof two normal distributions. We show that each step of the EM-algorithmincreases the log-likelihood of the observed data by maximizing the expectationof the log-likelihood for the complete data conditional on the observeddata. We determine explicit expressions for the maximization step in termsof simple conditional expectations and present an approach for determiningthe conditional expectations. Finally, by applying the algorithm to calibratethe jump diffusion model from Chapter 4, we demonstrate that the additionaljump component provides a significantly better model of the observed datathan a model without jumps and with only a single jump component.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/1pioq0f/alma99121979961605763

M3 - Ph.D. thesis

BT - Operation, Investment and Hedging in Electricity Markets

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -